where L is m-by-m lower triangular, Q is n-by-n
orthogonal (or unitary), Q1 consists of the first m rows of Q,
and Q2 the remaining n-m rows.

This factorization is computed by the routine xGELQF, and again Q is
represented as a product of elementary reflectors; xORGLQ
(or xUNGLQ in the complex case) can generate
all or part of Q, and xORMLQ (or xUNMLQ
) can pre- or post-multiply a given
matrix
by Q or QT (QH if Q is complex).

The LQ factorization of A is essentially the same as the QR factorization
of AT (AH if A is complex), since

The LQ factorization may be used to find a minimum norm solution of
an underdetermined system of linear equations A x = b where A is
m-by-n with m < n and has rank m. The solution is given by